A rancher wants to fence a rectangular pasture along a straight riverbank. He has 350 yards of fencing to enclose the other three sides of the pasture. If one side of the pasture has to be three times as long as the other, what is the area of the pasture? Find all possible answers. PLEASE LOOK AT THIS: The area can be ______ or _______ square yards. Thanks for answering!

Answers

Answer 1

Answer:

7500  or 14700 square yards

Step-by-step explanation:

Let the sides be x and y

3 sides sum to

2x + y = 350 orx + 2y = 350

If one side is 3 times the other then we have

x = 3y

The sums above become:

2x + y = 350 ⇒ 2(3y) + y = 350 ⇒ 7y = 350 ⇒ y = 50 and x = 150x + 2y = 350 ⇒ 3y + 2y = 350 ⇒ 5y = 350 ⇒ y = 70 and x = 210

The area in each case is:

50*150 = 7500 square yards70*210 = 14700 square yards

Related Questions

blem Read Aloud and Instructions Jada is looking to earn some extra money over summer break so she starts a babysitting service with some of her friends. The babysitting service charges a flat fee of $10 to book a babysitter and then charges a different amount per hour based on which person is babysitting. Jada earns d dollars per hour and works for h hours one night. Her total earnings, T. can be represented by the equation: T= dh + 10 Write the equation that can be used to easily find the amount of hours. h. Jada worked if we know her hourly rate, d, and her total earnings,

Answers

the equation of total earning by jada is

T = dh + 10

here, h = hours, d = dollars per hour, and T = total earning

Now,

\(\begin{gathered} T-10=dh \\ h=\frac{T-10}{d} \end{gathered}\)

so the answer is h = (T-10)/d

3 6 9 12 15 18 21 24 27 30 is odd or even numbers?​

Answers

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

3.
Cylinder A and Cylinder B are similar. Find the surface area of Cylinder B. Give
your answer in terms of .
Cylinder A
4 cm
Volume = 24T
Cylinder B
2 cm
PLEASE HELP!!

3.Cylinder A and Cylinder B are similar. Find the surface area of Cylinder B. Giveyour answer in terms

Answers

Volume of Cylinder B is,

⇒ V = 2.67π

We have to given that;

Two cylinders A nd B are shown in figure.

Here, In cylinder A;

Diameter = 4 cm

Volume of cylinder = 24π

Since, Volume of cylinder is,

V = πr²h

For cylinder A;

⇒ 24π = π (2²) × h

⇒ 24 / 4 = h

⇒ h = 6

Since, Cylinder A and B are similar.

Here, Height of B = 2 cm

And, Height of A = 6 cm

So, Scale factor is,

⇒ 6 / 2

⇒ 3

Hence, Radius of B  = 2/3

So, Volume of Cylinder B is,

⇒ V = π × (2/3)² × 2

⇒ V = 2.67π

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What is the best first step in solving m–2(m–4)≤3m for m? Distribute -2 through the parentheses. Add 4 to both sides of the inequality. Reverse the direction of the inequality sign. Subtract m from both sides of the inequality.

Answers

The best first step in solving m–2(m–4)≤3m for m will be A. Distribute -2 through the parentheses.

What is an inequality?

It should be noted that an inequality simply means a relation between the expressions that are unequal.

It should be noted that the best first step in solving m–2(m–4)≤3m for m will be to distribute -2 through the parentheses.

This is important in order to have variables of m and then solve accordingly.

In conclusion, the best option is A.

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If you plan to pay off a loan of $5,800 by submitting $250 per month, how many months will it take you to pay this debt off entirely and how much will your final payment be?

Answers

Answer:

24 months. Your final payment would be $50

Step-by-step explanation:

5800/250 gets you 23.2 but you can't have half of a month so, it would take 24 months. 250*23 makes 5750. 5800-5750 gets you 50. Your final payment would be $50

Answer: At least 24 months, with a final payment of 50 dollars on the 24th month.

Step-by-step explanation:

5,800/250 = 23.2

An easier way to do this is get this answer, and then multiply 250 by 23 which gives you ($)5,750, then just subtract that from $5,800 leaving you with 50, which is your last payment which is where the .2 comes from. Meaning it will take 24 months at the least, giving you $50 as your final payment.

1. Find the equation of the image of the circle x² + y2 + 16x-24y + 183 = 0 by rotated the line mirror 4x + 7y + 13 = 0. 2. The image of the circle (x - 3)² + (y-2)² = 1 in the line mirror ax + by = 19 is (x-1)³ + (y-16)2 = 1 then, find the values of (a, b). 3. Find the equation of a line passing through the origin and making an angle with the 4 line y-3x-5. 4. A parabola is drawn with its focus at (3,4) and vertex at the focus of the parabola y²-12x - 4y + 4 = 0. The n find equation of the parabola. 5. If the line ax + by + c = 0 touches the circle x² + y² - 2x = and is normal to the circle x² + y² + 2x - 4y + 1 = 0, then find the value of (a, b). 6. If the line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x. -3 7.1² 14 231= [] then find the matrix A 8. Find the equation of the ellipse having its center at the point (2,-3), one and one vertex at (4, -3). 3 9. Find the value of x if-1 0 10. Solve the linear system using Cramer's rule a) 2 1 2 4 (6x - 4y = -12 8x - 3y = -2 X = 16 -21 3x + 2y = z = 5 b) x-y+3z = -15 (2x + y +7z = -28 one focus at (3,-3) 11. Find the value of k for which the following system of linear equations has infinite solutions: x + (k+1)y = 5 ((k+1)x + 9y = 8k - 1​

Answers

Answer:

-72x - 53y + 287 = 0.

Step-by-step explanation:

To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.

The line mirror equation is given as 4x + 7y + 13 = 0.

The reflection of a point (x, y) in the line mirror can be found using the formula:

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

where A, B, and C are the coefficients of the line mirror equation.

For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.

Now, let's find the equations of the image of the circle.

The original circle equation is x² + y² + 16x - 24y + 183 = 0.

Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)

= (x - 8y - 8(4x + 7y + 13)) / 65

= (x - 8y - 32x - 56y - 104) / 65

= (-31x - 64y - 104) / 65

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)

= (y - 14x + 8(Ax + By + C)) / 65

= (y - 14x + 8(4x + 7y + 13)) / 65

= (57x + 35y + 104) / 65

Therefore, the equation of the image of the circle is:

(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0

Simplifying the equation, we get:

-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0

-72x - 53y + 287 = 0

So, the equation of the image of the circle is -72x - 53y + 287 = 0.

Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the health care system. The president wants the estimate to be within 0.02 of the true proportion. Assume a 99% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.41. A. How large of a sample is required? B b. How large of a sample would be necessary if no estimate were available for the proportion supporting current policy? (Round intermediate values to 3 decimal points. Round your answer up to the next whole number.)

Answers

The sample size for part A is 4025, and the sample size for part B is 4160

What is the margin of error(MOE)?

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

\(\rm MOE = Z\times \dfrac{s}{\sqrt{N}}\)

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            N is the number of samples.

MOE = 0.02

99% level of confidence

a = 1 - 0.99 = 0.01

Z(a/2) = 2.58

The president's political advisors estimated the proportion supporting the current policy to be 0.41.

A) p = 0.41

\(\rm N = p(1-p)(\dfrac{Z_{\alpha/2}}{MOE})^2\)

\(\rm N =0.41(1-0.41)(\dfrac{{2.58}}{0.02})^2\)

N = 4025.45 ≈ 4025

B) How large of a sample would be necessary if no estimate were available for the proportion supporting the current policy

\(\rm N =0.5(1-0.5)(\dfrac{{2.58}}{0.02})^2\)

N = 4160

Thus, the sample size for part A is 4025, and the sample size for part B is 4160

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a. Suppose a BMW dealer in Fullerton, CA is trying to calculate the probability of his car sale for next week. The dealer knows that the sale of car is normally distributed with mean 50 and variance 9. The variance 9 was calculated from the weekly car sale data of 20 weeks, as the population variance is not known to the dealer. What is the probability that the dealer will sell 51 or more cars next week? (Hint: use t distribution) (15)

Answers

Answer:

0.45576

Step-by-step explanation:

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Standard Deviation = √variance

Mean = 50

= √9

= 3

z = 51 - 50/3

= 0.11111

Probability value from Z-Table:

P(x<51) = 0.54424

P(x>51) = 1 - P(x<51)

= 1 - 0.54424

= 0.45576

The probability that the dealer will sell 51 or more cars is 0.45576

Why should you avoid investing all your money in familiar stocks?
A.
to increase the value of your returns
B.
to research unfamiliar industries that might reveal good investment opportunities
C.
to avoid selling at a loss
D.
to avoid diversifying into multiple investment options

Answers

Answer:

B.

Step-by-step explanation:

The main reason for this is to research unfamiliar industries that might reveal good investment opportunities. When you conform to what you know, you fall into a comfort zone. This prevents you from taking the time to investigate and learn new things. In this scenario, investing everything in familiar stocks will prevent you from looking for new investment options in different industries which could have led to incredible investment opportunities. Therefore, it is a better choice to invest a large portion in safer familiar stocks but leave a certain percentage for riskier and newer investments.

Answer:

Why should you avoid investing all your money in familiar stocks?

A.

to increase the value of your returns

B.

to research unfamiliar industries that might reveal good investment opportunities

C.

to avoid selling at a loss

D.

to avoid diversifying into multiple investment options

Step-by-step explanation:

A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.

Answers

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

Finding the equation perpendicular to the tangent

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

The smallest slope on the curve

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

The equation of the tangent line

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Since insulin u-100 is 100 units/mL,which of the following shortcuts can be used to convert a dose of u-100 insulin given in units, to mL

Answers

Answer:

The shortcuts is

     Divide number of units by 100

Step-by-step explanation:

From the question we are told that

  insulin u-100 is  \(L = 100 \ unit /mL\)

 From the data given above we see that

           100 units of  insulin u-100 is contained in  1 mL

So         1 unit of  u-100 is contained in  x mL

=>       \(x = \frac{1}{100} \ mL\)

This means that a unit of  insulin u-100 occupies  \(x = \frac{1}{100} \ mL\)

So we can represent a single unit of insulin u-100 as  \(\frac{1}{100} \ mL\)

  Now if 1 unit of insulin u-100 is represented  as    \(\frac{1}{100} \ mL\)

Then y unites of   insulin u-100  is represented as  z

So

         \(z = \frac{y}{100} \ mL\)

From the above calculation we can see that the shortcuts to convert  u-100 insulin given in units, to mL is to  divide  number of units by 100

                       

I’ve attached a photo
Solve for n:
3/4f-5/2n=2
n=

Ive attached a photoSolve for n:3/4f-5/2n=2n=

Answers

Answer:

\(n=\frac{3f-8}{10}\)

Step-by-step explanation:

So we have the equation:

\(\frac{3}{4}f-\frac{5}{2}n=2\)

First, remove all the fractions by multiplying by the LCM of the denominator.

The LCM of 4 and 2 is 4. Thus:

\(4(\frac{3}{4}f-\frac{5}{2}n)=4(2)\)

Distribute:

\(4(\frac{3}{4}f})-4(\frac{5}{2}n})=4(2)\)

Simplify:

\(3f-10n=8\)

Subtract 3f from both sides:

\((3f-10n)-3f=(8)-3f\\-10n=8-3f\)

Divide both sides by -10:

\(n=\frac{8-3f}{-10}\)

Divide by -1:

\(n=\frac{3f-8}{10}\)

And this is our answer :)

Answer:

n = (3f - 8)/10

Step-by-step explanation:

3f/4 - ²⁾5n/2 = ⁴⁾2

3f - 10n = 8

3f - 8 = 10n

n = (3f - 8)/10

*REVERSE PROPORTION*

*REVERSE PROPORTION*

Answers

9514 1404 393

Answer:

  33.3%

Step-by-step explanation:

The selling price of £42 is (1 +40%) times the total purchase price.

  1.40 × purchase price = £42

  purchase price = £42/1.40 = £30

The total profit is 40% of this, so is ...

  £30 × 40% = £12

The purchase price of the skirt is ...

  total cost - glove cost = skirt cost = £30 -3 = £27

The profit on the skirt is ...

  total profit - glove profit = skirt profit = £12 -100% × £3 = £9

Then the percentage profit on the skirt is ...

  skirt profit % = skirt profit / skirt cost × 100% = £9/£27 × 100% = 33.3%

The percentage profit on the cost of the skirt was 33.3%.

7a+1+3=18


Please answer quickly!

Answers

Answer:

2

Step-by-step explanation:

So we have the equation:

\(7a+1+3=18\)

Add 1 and 3:

\(7a+4=18\)

Subtract 4 from both sides:

\(7a=14\)

Divide both sides by 7:

\(a=2\)

And we're done!

7a+1+3=18

combine like terms.

7a+4=18

subtract 4 from 18

7a=14

divide 14 by 7

a=2


Please answer quickly!

A store gives a 15% discount to reward members? What is the discount on $215 worth of merchandise

Answers

To find the discount on $215 worth of merchandise with a 15% discount, you can use the following steps:

1. Calculate the discount amount as a percentage of the original price:

discount amount = original price x discount rate

discount amount = $215 x 0.15

discount amount = $32.25

2. Subtract the discount amount from the original price to find the sale price:

sale price = original price - discount amount

sale price = $215 - $32.25

sale price = $182.75

Therefore, the discount on $215 worth of merchandise with a 15% discount is $32.25. The sale price after the discount is $182.75.

Status
Recovery
ZABD and ZDBC are supplementary angles.
What is the measure of x?
X = [?]°
7D
110%
AK
B.
→C
Angles are not drawn to scale.
Enter

StatusRecoveryZABD and ZDBC are supplementary angles.What is the measure of x?X = [?]7D110%AKB.CAngles

Answers

Answer:

jhbujnhjnv

Step-by-step explanation:

vnjhbjhbjmb

Answer:

x=70°

Step-by-step explanation:

x+110=180 linear pair

x=180-110=70

Find the general solution of the differential equation.
6y (4) +83y" +100y = 0
y(x) =

Answers

Refer to the attached image.

Find the general solution of the differential equation.6y (4) +83y" +100y = 0y(x) =
Find the general solution of the differential equation.6y (4) +83y" +100y = 0y(x) =

answer correct plz if u steal points ill report

answer correct plz if u steal points ill report

Answers

Answer:

In my knowledge

Option A

and I am 100% sure

explanation:

Continuous graphs are graphs where there is a value of y for every single value of x, and each point is immediately next to the point on either side of it so its option A

Answer:

Step-by-step explanation:

add me brainliest

answer correct plz if u steal points ill report

θ is an acute angle. Find the value of θ in degrees.
sec(θ)=2

Answers

The value of θ is 60° and the the value of the equation sec 60° = 2

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the angle be represented as θ

Now , given that the angle θ is acute

Acute angles measure less than 90 degrees

So , the value of θ < 90°

when the value of sec θ = 2

cos θ = 1/sec θ

So , cos θ = 1/2

The value of θ when cos θ is 1/2 is when the angle θ is 60°

Therefore , the value of θ is 60° and sec 60° = 2

Hence , The value of θ is 60° and the the value of the equation sec 60° = 2

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When two lines intersect, they intersect at a...
A) Ray
B
Point
Line
Plane

Answers

Answer:

point

Step-by-step explanation:

What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4?

What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K

Answers

The x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4 is (17, 11)

Midpoint of coordinate points

The midpoint of a line is the point that bisects or divides the line into two equal parts

If the line JK is partitioned into the ratio 1:4 with the following coordinates

J(-15, -5) and K(25, 15)

Using the expression below;

M(x, y) =[mx1+nx2/m+n, my1+ny2/m+n]

Substitute the ratio and the coordinates

M(x, y) =[1(-15)+4(25)/4+1, 1(-5)+4(15)/1+4]

M(x, y) = [(85)/5, 55/5]

M(x, y) = (17, 11)

Hence the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4 is ((17, 11)

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Use the long division method to find the result when 82% + 28x2 + 14x – 13 is
+
divided by 2x + 3. If there is a remainder, express the result in the form
r(3)
9(x) +
b(a)'

Answers

Answer:

Step-by-step explanation:

Free brainliest to the first who answers and 100 points!!!!! also a thanks and a five star

Find the coordinates of the centroid of ️RST with vertices R(-5,-9), S(6,-3), T(-1,6)

Answers

The coordinates of the centroid of the triangle RST is (0, -2)

What is a triangle?

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The coordinates of the vertices of the triangle RST:

R(-5,-9), S(6,-3), T(-1,6)

The coordinates (x, y) of the centroid of a triangle.

x = (a + c + e) / 3

y = (b + d + f) / 3

Where (a, b), (c, d), and (e, f) are the coordinates of the vertices of a triangle.

Now,

(a, b) = (-5, -9)

(c, d) = (6, -3)

(e, f) = (-1, 6)

The coordinates (x, y) of the centroid of a triangle is (0, -2).

x = (-5 + 6 - 1) / 3

x = 0

y = (-9 - 3 + 6) / 3

y = -6/3

y = -2

Thus,

The coordinates of the centroid are (0, -2).

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Help help help meeee

Help help help meeee

Answers

Answer:

is C you're welcome!!!!!

leslie has 3 boxes of tea in her cupboard. each box contains 11 tea bags. each tea bag makes 3 cups of hot tea. how many cups of tea will leslie make if she uses all the tea bags

Answers

Answer:

99

Step-by-step explanation:

3x11=33x3cups=99

Find the mean for the data set. 19, 17, 17, 17, 17, 17, 13, 15, 16, 22, 18

Answers

Answer:

The mean is 17.091

Step-by-step explanation:

Ms. Perkins asked her students to label a base b and corresponding height h. Use the triangles below to show three possible ways to do this.

Answers

Three ways to label a base (b) and corresponding height (h) are:

1. Base as the bottom side, height as a perpendicular line segment.

2. Base as a side, height as a perpendicular line segment.

3. Base as the hypotenuse, height as a perpendicular line segment.

To label a base (b) and corresponding height (h), three possible ways can be demonstrated using the triangles below:

1. Triangle 1:

  - Base (b) is labeled as the bottom side of the triangle.

  - Height (h) is labeled as a vertical line segment perpendicular to the base, connecting the opposite vertex to the base.

2. Triangle 2:

  - Base (b) is labeled as the side of the triangle.

  - Height (h) is labeled as a vertical line segment perpendicular to the base, connecting the opposite vertex to the base.

3. Triangle 3:

  - Base (b) is labeled as the hypotenuse (the longest side) of the triangle.

  - Height (h) is labeled as a vertical line segment drawn from one of the vertices of the base, perpendicular to the base.

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PLEASE HELP ASAP I WILL GIVE BRAINLIEST

PLEASE HELP ASAP I WILL GIVE BRAINLIEST

Answers

Answer:

Step-by-step explanation:

y^(7/8 - 2/8) = y^5/8

Option 1 is the answer

What is the volume of this figure?

Enter your answer in the box.

yd³

What is the volume of this figure?Enter your answer in the box. yd

Answers

The volume of the composite figure is

4095 cubic yd

How to find the volume of the composite figure

The volume is calculated by dividing the figure into simpler shapes. and adding the individual volumes

The simple shapes used here include

trapezoid andrectangle

Volume of rectangle = length x width x depth

= 30 * 9 * 7

= 1890 cubic yd

Volume of trapezoid = 1/2 (sum of parallel lines) x height x depth

= 1/2 (30 + 19) x 10 x 9

= 2205 cubic  yd

Total volume

= 1890 cubic yd + 2205 cubic yd

=  4095 cubic yd

Learn more about composite shapes at

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How do I find GBA and show all the work

How do I find GBA and show all the work

Answers

Answer:

Angle ACB = 44°

There are two ways to solve it. Both are right

Solution number 1

From triangle ABC

angle BAC = 180°-(102° +44°) = 36°

Because BG is parallel with AC

Then angle GBA = angle BAC = 34°

Another solution

The sum of angles in the shape AGBC = 360°

So angle GBC = 360 - (90 + 90 + 44 + 102) = 34°

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